Unified approach to Čerenkov second harmonic generation

Roppo, Vito; Kalinowski, Ksawery; Sheng, Yan; Królikowski, Wiesław; Cojocaru, C.; Trull, J.

doi:10.1364/oe.21.025715

Cited by 28 publications

(25 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The difference in the pulse duration obtained with both methods has not exceeded 2%. This difference is consistent with the resolution error introduced by our experimental setup taking into account the parameters of the CCD camera, the intersection angle α and the propagation errors in the formulas (8) and (9). For the parameters used in our experiment we obtained an error estimation of around 5% for the pulse duration and of the order of 10% for the chirp determination.…”

Section: (T)=e O (T)exp(-iω O T) With: (3)supporting

confidence: 87%

“…While the reversed orientation of domains corresponds to inversion of sign of the quadratic susceptibility, the refractive index of these crystals remains practically homogeneous [7]. Such crystals provide phase matching for frequency conversion processes over wide angular and frequency bandwidths without need for angular or temperature tuning as it is usual in typically used homogeneous nonlinear crystals [8][9][10]. Phase matching is obtained thanks to the continuous set of reciprocal lattice vectors, G, arising from the random size and distribution of the nonlinear domains, which entails a random distribution of the nonlinearity sign.…”

mentioning

confidence: 99%

“…The width of this AC trace , Δz, is directly related to the pulse duration. Assuming a Gaussian beam profile of the input pulses, the intensity of the AC signal is given by the expression [9]:…”

mentioning

confidence: 99%

See 2 more Smart Citations

Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal

Trull

Sola

Wang

et al. 2015

Applied Physics Letters

View full text Add to dashboard Cite

Pulse compression in dispersive Strontium Barium Niobate (SBN) crystal with a random size and distribution of the antiparallel orientated nonlinear domains is observed via transverse second harmonic generation. The dependence of the transverse width of the second harmonic trace along the propagation direction allows for the determination of the initial chirp and duration of pulses in the femtosecond regime. This technique permits a real-time analysis of the pulse evolution and facilitates fast in-situ correction of pulse chirp acquired in the propagation through an optical system. Ultrashort laser pulses, with their variety of peak powers and durations, are becoming an important tool in an increasing number of applications in the fields of technology (materials processing, etc.) biomedical sciences and basic research in general. As the pulses become shorter, the dispersion effects that modify pulse properties during propagation through optical materials become increasingly relevant so a precise characterization of the pulse properties is needed. During the last decade different techniques have been implemented and extensively adopted [1][2][3][4] either for partial or/and complete temporal characterization of the pulses. They include for instance, Frequency-Resolved Optical Gating (based on the concept of optical gating) or Spectral Phase Interferometry for Direct Electric-field Reconstruction, (based on the concept of spectral interferometry) or even for 3D characterization (STARFISH, SEA Tadpole) [5][6]. Although a detailed field reconstruction is needed in particular applications and thus fully justifies the use of these advanced techniques, there are still many situations requiring just a partial characterization of the pulse. Hence simple and cost-effective methods of pulse measurement and characterization are always of potential interest.Typical as-grown ferroelectric crystals, such as Strontium Barium Niobate (SBN), exhibit a random-sized distribution of needele-like oppositely oriented ferroelectric domains all aligned parallel to the optical axis (z axis). A shematic representation of such domains is shown in Figure 1a. While the reversed orientation of domains corresponds to inversion of sign of the quadratic susceptibility, the refractive index of these crystals remains practically homogeneous [7]. Such crystals provide phase matching for frequency conversion processes over wide angular and frequency bandwidths without need for angular or temperature tuning as it is usual in typically used homogeneous nonlinear crystals [8][9][10]. Phase matching is obtained thanks to the continuous set of reciprocal lattice vectors, G, arising from the random size and distribution of the nonlinear domains, which entails a random distribution of the nonlinearity sign. These lattice vectors, with different modulus and orientation, lie in the xy plane. As a result, planar second harmonic emission is observed when the input fundamental beam propagates in the direction perpendicular to the optical axis. This effect consti...

show abstract

Section: (T)=e O (T)exp(-iω O T) With: (3)supporting

confidence: 87%

mentioning

confidence: 99%

See 1 more Smart Citation

Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal

Trull

Sola

Wang

et al. 2015

Applied Physics Letters

View full text Add to dashboard Cite

show abstract

“…However, because of the randomness in the domain distribution, this is no longer the case. As discussed earlier [23], the randomness in a nonlinear crystal leads to the incoherent buildup of generated waves. As a result, the two constituent processes in the SHG are mutually incoherent.…”

mentioning

confidence: 83%

Calcium barium niobate as a functional material for broadband optical frequency conversion

et al. 2014

Self Cite

View full text Add to dashboard Cite

We demonstrate the application of as-grown calcium barium niobate (CBN) crystal with random-sized ferroelectric domains as a broadband frequency converter. The frequency conversion process is similar to broadband harmonic generation in commonly used strontium barium niobate (SBN) crystal, but results in higher conversion efficiency reflecting a larger effective nonlinear coefficient of the CBN crystal. We also analyzed the polarization properties of the emitted radiation and determined the ratio of d 32 and d 33 components of the second-order susceptibility tensor of the CBN crystal.Ferroelectric crystal has been exploited in a wide range of devices since its discovery in the 1920s [1]. These devices include filters for wireless communications, modulators in optical circuits, and optical frequency converters in laser technology. Most of these functions are based on 180°antiparallel ferroelectric domains and the ability to engineer these domains on the micro or submicroscale [2]. Of the many ferroelectrics, those asgrown with random-sized ferroelectric domains form a unique group. As far as application in nonlinear optics is concerned, the random domain pattern results in a spatially random modulation of the quadratic nonlinearity of the material. Thus, a pool of reciprocal lattice vectors with random orientations and random magnitudes is created to phase match nonlinear interactions over a broad spectrum of wavelengths. Such a technique is known as random quasi-phase matching (QPM) [3][4][5].A good case in point is strontium barium niobate (Sr x Ba 1−x Nb 2 O 6 , SBN) crystal, which has been commonly used for broadband second harmonic generation (SHG) [6], cascaded third harmonic generation [7,8], and even Čerenkov-type nonlinear interactions [9][10][11]. However, the phase transition temperature (Curie temperature, T c ) of the SBN crystal is low [12], which is a main drawback for laser applications. At high pump power, the crystal will undergo a transition to the paraelectric state, and consequently, the quadratic nonlinear optical effects will disappear [13]. Compared with SBN, calcium barium-niobated (Ca x Ba 1−x Nb 2 O 6 , CBN) crystal is more suitable for practical optical devices operating at higher pump powers because of its higher phase transition temperature. For example, the CBN crystal exhibits a transition temperature of about 539 K for the congruently melting composition with 28 mol. % of calcium (x 0.28, CBN-28) [14,15], but the SBN crystal shows a lower transition temperature of about 353 K for the congruently melting composition with 61 mol. % of strontium content (x 0.61, SBN-61) [16,17]. Recently, Čerenkov-type SHG has been demonstrated in the CBN-28 crystal, which can be used as a nonlinear prism [18][19][20].In this Letter, we show that the CBN crystal is superior over the traditional SBN crystal in terms of the frequency mixing process, which leads to a higher conversion efficiency. We demonstrate experimentally that the broadband SHG process in the CBN crystal is three to four times higher ...

show abstract

“…However, for the NBD process to occur, both LPM and TPM need to be satisfied. In the past twenty years, secondharmonic generation (SHG) via various nonlinear diffractions in 1D and 2D NPCs had been the major focus [7][8][9][10][11][12][13] . Although high-order harmonics (HH) are very important to the field of nonlinear optics, until recently, publications on HH generation using NPCs have been almost nonexistent.…”

mentioning

confidence: 99%

Fourth-harmonic generation via nonlinear diffraction in a 2D LiNbO3 nonlinear photonic crystal from mid-IR ultrashort pulses

Kafka

Chowdhury

2017

中国光学快报

View full text Add to dashboard Cite

Five conical harmonic beams are generated from the interaction of femtosecond mid-infrared (mid-IR) pulses at a nominal input wavelength of 1997 nm with a 2D LiNbO 3 nonlinear photonic crystal with Sierpinski fractal superlattices. The main diffraction orders and the corresponding reciprocal vectors involved in the interaction are ascertained. Second and third harmonics emerging at external angles of 23.82°and 36.75°result from nonlinearČerenkov and Bragg diffractions, respectively. Three pathways of fourth-harmonic generation are observed at external angles of 14.21°, 36.5°, and 53.48°, with the first one resulting from nonlinearČerenkov diffraction, and the other two harmonics are generated via different cascaded processes.OCIS codes: 190.4420, 190.2620, 050.1940. doi: 10.3788/COL201715.051901.When a monochromatic wave passes through a homogeneous medium with its second-order nonlinear susceptibility varying in some regions, e.g., χ ð2Þ in a nonlinear photonic crystal (NPC), nonlinear diffraction can be detected for the harmonic rings or spots of the input fundamental wave [1][2][3][4][5][6] . Nonlinear diffraction, which is based on phase matching, includes nonlinearČerenkov diffraction (NCD), nonlinear Raman-Nath diffraction (NRND), and nonlinear Bragg diffraction (NBD). For NCD, the longitudinal phase matching (LPM) is satisfied when the longitudinal direction is parallel to the incident fundamental laser beam. This phase matching can be achieved by the addition of integer multiples of the incident wave vector or the combination of the incident wave vector and reciprocal vectors. In the case of NRND, the transverse (perpendicular to the incident fundamental laser beam) phase matching (TPM) has to be satisfied. This can be achieved by the combination of the reciprocal vectors. However, for the NBD process to occur, both LPM and TPM need to be satisfied. In the past twenty years, secondharmonic generation (SHG) via various nonlinear diffractions in 1D and 2D NPCs had been the major focus [7][8][9][10][11][12][13] . Although high-order harmonics (HH) are very important to the field of nonlinear optics, until recently, publications on HH generation using NPCs have been almost nonexistent. Recently, there have been several significant efforts to generate third harmonics in periodic, short-range ordered or radially poled NPCs, NPC waveguide and random quadratic media by NCD and NRND [14][15][16][17][18] . Also, high efficiency quasi-phase-matched harmonic generation from the 2nd to 8th order have been observed within a single LiNbO 3 (LN) NPC [19] . However, fourth-harmonic generation (FHG) via nonlinear diffraction is rarely reported. The advantage of using a 2D fractal superlattice is that it may allow the freedom of optimization of many parameters such as input wavelength, harmonic order, angle, and efficiency. In this Letter, second, third, and especially multiple fourth harmonics are achieved by nonlinear diffractions in an LN NPC with Sierpinski fractal superlattices under femtosecond pulses.In our experim...

show abstract

Unified approach to Čerenkov second harmonic generation

Cited by 28 publications

References 35 publications

Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal

Ultrashort pulse chirp measurement via transverse second-harmonic generation in strontium barium niobate crystal

Calcium barium niobate as a functional material for broadband optical frequency conversion

Fourth-harmonic generation via nonlinear diffraction in a 2D LiNbO3 nonlinear photonic crystal from mid-IR ultrashort pulses

Contact Info

Product

Resources

About